Question

A grinding wheel is spinning with an initial angular velocity +ω0. When its motor is turned off at t=0, it begins to slow down with an angular acceleration −α. Derive an expression for the number of revolutions that the wheel will rotate through before coming to rest. Express your answer in terms of the variables ω0 and α, and the constant π.

Answer 1

Answer:

Explanation:

Given

initial angular velocity is $\omega _0$

when motor is turned of it started decelerating with $-\alpha$  angular acceleration

angle turned before coming to halt

$\omega ^2-\omega _0^2=2(\alpha )\theta$

here final angular velocity is zero

$-\omega _0^2=-2\alpha \theta$

$\theta =\frac{\omega _0^2}{2\alpha }$

No of revolutions will be $N=\frac{\theta }{2\pi }$

$N=\frac{\omega _0^2}{4\pi \alpha }$